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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 <span class="keyword">from</span> cvxopt <span class="keyword">import</span> matrix, spmatrix
<a name="l00004"></a>00004 <span class="keyword">from</span> cvxopt.blas <span class="keyword">import</span> gemv
<a name="l00005"></a>00005 <span class="keyword">from</span> cvxopt.solvers <span class="keyword">import</span> qp
<a name="l00006"></a>00006 
<a name="l00007"></a>00007 
<a name="l00008"></a>00008 <span class="comment">#\begin{array}{ll} \mbox{minimize} &amp; 2x_1^2 + x_2^2 + x_1 x_2 + x_1 + x_2 \\ \mbox{subject to} &amp; x_1 \geq 0 \\ &amp; x_2 \geq 0 \\ &amp; x_1 + x_2 = 1 \end{array}</span>
<a name="l00009"></a>00009 <span class="comment">#http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html</span>
<a name="l00010"></a>00010 Q = 2*matrix([ [2, .5], [.5, 1] ])
<a name="l00011"></a>00011 p = matrix([1.0, 1.0])
<a name="l00012"></a>00012 G = matrix([[-1.0,0.0],[0.0,-1.0]])
<a name="l00013"></a>00013 h = matrix([0.0,0.0])
<a name="l00014"></a>00014 A = matrix([1.0, 1.0], (1,2))
<a name="l00015"></a>00015 b = matrix(1.0)
<a name="l00016"></a>00016 sol=qp(Q, p, G, h, A, b)
<a name="l00017"></a>00017 
<a name="l00018"></a>00018 <span class="keyword">def </span>append_matrix_at_bottom(A, B):
<a name="l00019"></a>00019     l = []
<a name="l00020"></a>00020     <span class="keywordflow">for</span> x <span class="keywordflow">in</span> xrange(A.size[1]):
<a name="l00021"></a>00021         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> xrange(A.size[0]):
<a name="l00022"></a>00022             l.append(A[i + x * A.size[0]])
<a name="l00023"></a>00023         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> xrange(B.size[0]):
<a name="l00024"></a>00024             l.append(B[i + x * B.size[0]])
<a name="l00025"></a>00025     <span class="keywordflow">return</span> matrix(l, (A.size[0] + B.size[0], A.size[1]))
<a name="l00026"></a>00026 
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 M = matrix([[4.0, 6, -4, 1.0], [6, 1, 1.0, 2.0], [-4, 1.0, 2.5, -2.0],
<a name="l00029"></a>00029            [1.0, 2.0, -2.0, 1.0]])
<a name="l00030"></a>00030 q = matrix([12, -10, -7.0, 3])
<a name="l00031"></a>00031 
<a name="l00032"></a>00032 I = spmatrix(1.0, range(M.size[0]), range(M.size[1]))
<a name="l00033"></a>00033 G = append_matrix_at_bottom(-M, -I)  <span class="comment"># inequality constraint G z &lt;= h</span>
<a name="l00034"></a>00034 
<a name="l00035"></a>00035 h = matrix([x <span class="keywordflow">for</span> x <span class="keywordflow">in</span> q] + [0.0 <span class="keywordflow">for</span> _x <span class="keywordflow">in</span> range(M.size[0])])
<a name="l00036"></a>00036 
<a name="l00037"></a>00037 sol = qp(2.0 * M, q, G, h)  <span class="comment"># find z, w, so that w = M z + q</span>
<a name="l00038"></a>00038 <span class="keywordflow">if</span> sol[<span class="stringliteral">&#39;status&#39;</span>] == <span class="stringliteral">&#39;optimal&#39;</span>:
<a name="l00039"></a>00039     z = sol[<span class="stringliteral">&#39;x&#39;</span>]
<a name="l00040"></a>00040     w = matrix(q)
<a name="l00041"></a>00041     gemv(M, z, w, alpha=1.0, beta=1.0)  <span class="comment"># w = M z + q</span>
<a name="l00042"></a>00042     <span class="keywordflow">print</span> z
<a name="l00043"></a>00043     <span class="keywordflow">print</span> w
<a name="l00044"></a>00044 <span class="keywordflow">else</span>:
<a name="l00045"></a>00045     <span class="keywordflow">print</span> <span class="stringliteral">&#39;failed&#39;</span>
<a name="l00046"></a>00046 <span class="comment">#http://en.wikipedia.org/wiki/Linear_complementarity_problem</span>
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